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Global well-posedness and blow-up on the energy space for the inhomogeneous nonlinear Schrödinger equation

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Abstract

We consider the supercritical inhomogeneous nonlinear Schrödinger equation

$$i\partial_t u+\Delta u+|x|^{-b}|u|^{2\sigma}u=0,$$

where \({(2 - b)/N < \sigma < (2 - b)/(N-2)}\) and \({0 < b < \rm min\{2,N\}}\). We prove a Gagliardo–Nirenberg-type estimate and use it to establish sufficient conditions for global existence and blow-up in \({H^1(\mathbb{R}^N)}\).

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Authors and Affiliations

  1. ICEx, Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627, Caixa Postal 702, 30123-970, Belo Horizonte-MG, Brazil

    Luiz G. Farah

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  1. Luiz G. Farah
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Correspondence to Luiz G. Farah.

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Farah, L.G. Global well-posedness and blow-up on the energy space for the inhomogeneous nonlinear Schrödinger equation. J. Evol. Equ. 16, 193–208 (2016). https://doi.org/10.1007/s00028-015-0298-y

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